Multidimensional stability analysis of gaseous detonations near Chapman–Jouguet conditions for small heat release

Abstract

Multidimensional instability of planar detonations, leading to cellular structures, is studied analytically near Chapman–Jouguet conditions, in the limit of small heat release, with small (Newtonian) differences between heat capacities, by using an expansion in a small parameter representing the ratio of the heat release to the thermal enthalpy of the fresh mixture. In this limit, the dynamics of detonations is governed by the interaction between the acoustic waves and the heat-release rate inside the inner detonation structure, the entropy–vorticity wave playing a negligible role at leading order. This situation is just opposite from that considered in our 1997 study of strongly overdriven detonations. The present analysis offers a step towards improving our understanding of the cellular structures of ordinary detonations, for which both the entropy–vorticity waves and the acoustic waves are involved in the instability mechanism. The relevant bifurcation parameter is identified, involving the degree of overdrive and the sensitivity of the rate of heat release to temperature at the Neumann state, and the onset of the instability is studied analytically for a realistic model of the inner structure of gaseous detonations.